A Particle Fokker-Planck Algorithm with Multiscale Temporal Discretization for Rarefied and Continuum Gas Flows (Communications in Computational Physics, 2018)
For gas flows with moderate and low Knudsen numbers, pair-wise collisionsin the Boltzmann equation can be approximated by the Langevin model correspondingto the Fokker-Planck equation. Using this simplified collision model, particlenumerical schemes, e.g. the Fokker-Planck model (FPM) method, can simulatelow Knudsen number gas flows more efficient than those based on the Boltzmannequation, such as the Direct Simulation Monte Carlo (DSMC) method. However, asanalyzed in this paper, the transport properties of the FPM method deviate from thephysical values as the time step increases, and this problem affects its computationalaccuracy and efficiency for the simulation of multi-scale flows. Here we propose a particleFokker-Planck algorithm with multiscale temporal discretization (MTD-FPM) toovercome the drawbacks of the original FPM method. In the MTD-FPM method, themolecular motion is tracked following the integration scheme of the Langevin modelin analogy to the original FPM method. However, to ensure consistent transport coefficientsfor arbitrary temporal discretization, a time step dependent friction coefficienthas been implemented. Several benchmark problems, including Couette, thermal Couette,Poiseuille, and Sod tube flows, are simulated to validate the proposed MTD-FPMmethod.